{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using ITensorMPS\n",
    "using ITensors\n",
    "using Plots\n",
    "using DelimitedFiles\n",
    "using ITensorEntropyTools"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Find Ground State"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "After sweep 1 energy=-17.414482894677366  maxlinkdim=10 maxerr=3.62E-03 time=0.019\n",
      "After sweep 2 energy=-17.41449342736761  maxlinkdim=11 maxerr=1.00E-10 time=0.014\n",
      "After sweep 3 energy=-17.414493427328445  maxlinkdim=10 maxerr=7.85E-11 time=0.009\n",
      "After sweep 4 energy=-17.414493427358757  maxlinkdim=10 maxerr=7.49E-11 time=0.010\n",
      "After sweep 5 energy=-17.41449342736052  maxlinkdim=10 maxerr=7.49E-11 time=0.012\n",
      "After sweep 6 energy=-17.414493427360508  maxlinkdim=10 maxerr=7.48E-11 time=0.009\n",
      "After sweep 7 energy=-17.41449342736047  maxlinkdim=10 maxerr=7.46E-11 time=0.011\n",
      "After sweep 8 energy=-17.414493427360433  maxlinkdim=10 maxerr=7.45E-11 time=0.009\n",
      "After sweep 9 energy=-17.41449342736044  maxlinkdim=10 maxerr=7.44E-11 time=0.012\n",
      "After sweep 10 energy=-17.414493427360462  maxlinkdim=10 maxerr=7.44E-11 time=0.012\n",
      "After sweep 11 energy=-17.414493427360412  maxlinkdim=10 maxerr=7.43E-11 time=0.009\n",
      "After sweep 12 energy=-17.414493427360455  maxlinkdim=10 maxerr=7.43E-11 time=0.012\n",
      "After sweep 13 energy=-17.414493427360433  maxlinkdim=10 maxerr=7.43E-11 time=0.010\n",
      "After sweep 14 energy=-17.414493427360462  maxlinkdim=10 maxerr=7.43E-11 time=0.008\n",
      "After sweep 15 energy=-17.41449342736042  maxlinkdim=10 maxerr=7.43E-11 time=0.010\n"
     ]
    }
   ],
   "source": [
    "N_s = 16\n",
    "sites = siteinds(\"S=1/2\", N_s+4)\n",
    "\n",
    "J = 0.4\n",
    "h = 1\n",
    "g = 0.05\n",
    "\n",
    "\n",
    "os = OpSum()\n",
    "for j=1:N_s\n",
    "    if j == N_s\n",
    "        os -= J, \"X\", j, \"X\", 1\n",
    "        os -= g, \"Z\", j, \"Z\", 1\n",
    "    else\n",
    "        os -= J, \"X\", j, \"X\", j+1\n",
    "        os -= g, \"Z\", j, \"Z\", j+1\n",
    "    end\n",
    "    os -= h, \"Z\", j\n",
    "end\n",
    "H = MPO(os, sites)\n",
    "\n",
    "psi0 = randomMPS(sites; linkdims=2^7)\n",
    "\n",
    "nsweeps = 15\n",
    "maxdim = [10,20,100,100,200]\n",
    "cutoff = [1E-10]\n",
    "noise = [1E-6]\n",
    "weight = 50\n",
    "\n",
    "energy0,psi0 = dmrg(H,psi0;nsweeps,maxdim,cutoff)\n",
    "\n",
    "for i in N_s+1:N_s+4\n",
    "    if mod(i, 2) == 0\n",
    "        proj_tensor = op(sites[i], \"ProjUp\")\n",
    "    else\n",
    "        proj_tensor = op(sites[i], \"ProjDn\")\n",
    "    end\n",
    "    psi0 = apply(proj_tensor, psi0)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.018573900673054533, 0.01857373084824815, 0.018574262075068015, 0.0185743096357725, 0.018574314970314976, 0.018574315562948363, 0.018574315716707923, 0.018574315634452443, 0.018574315670512265, 0.018574315839038236, 0.01857431571122997, 0.01857431515504948, 0.018574309797457056, 0.01857426213269825, 0.01857373095512188, 0.018573900626103867, 1.0000000000000009, -9.992007221626409e-16, 1.0000000000000009, -9.992007221626409e-16]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "magz = expect(psi0, \"Z\")\n",
    "occs = [(1 - magz[n])/2 for n=1:N_s+4]\n",
    "println(occs)\n",
    "\n",
    "sites = [n for n=1:N_s+4]\n",
    "plot(bar(sites, occs; label=\"TEBD\"), xlabel=\"site (s)\", ylabel=\"Occupation Number\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Two-Particle Scattering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "giv_op (generic function with 1 method)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "function rz(theta::Float64, i::Int, psi::MPS, cutoff::Float64)\n",
    "    s = siteinds(psi)\n",
    "    z_i = op(\"Z\", s[i])\n",
    "    Op = exp(-1im/2 * theta * z_i)\n",
    "    psi = apply(Op, psi; cutoff)\n",
    "    return psi\n",
    "end\n",
    "\n",
    "function giv_op(theta::Float64, i::Int, j::Int, psi::MPS, cutoff::Float64)\n",
    "    s = siteinds(psi)\n",
    "    x_i = op(\"X\", s[i])\n",
    "    y_i = op(\"Y\", s[i])\n",
    "    x_j = op(\"X\", s[j])\n",
    "    y_j = op(\"Y\", s[j])\n",
    "    Op = x_i * y_j - x_j * y_i\n",
    "    Op = exp(1im * theta / 2 * Op)\n",
    "    psi = apply(Op, psi; cutoff)\n",
    "    return psi\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7-element Vector{Float64}:\n",
       " -0.04452199\n",
       " -0.10805302\n",
       " -0.25917978\n",
       " -0.58569283\n",
       " -1.0800755\n",
       " -1.4472062\n",
       " -1.55743797"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "betas_r = [-2.15984495, -0.78539816,  0.58904862,  1.96349541, -2.94524311,\n",
    "       -1.57079633, -0.19634954,  1.17809725]\n",
    "thetas_r = [-0.04452199, -0.10805302, -0.25917978, -0.58569283, -1.0800755 ,\n",
    "       -1.4472062 , -1.55743797]\n",
    "\n",
    "betas_l = [-2.55254403,  2.35619449,  0.9817477 , -0.39269908, -1.76714587,\n",
    "       -3.14159265,  1.76714587,  0.39269908]\n",
    "thetas_l = [-0.04452199, -0.10805302, -0.25917978, -0.58569283, -1.0800755 ,\n",
    "       -1.4472062 , -1.55743797]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "cutoff = 1E-8\n",
    "\n",
    "n_kr = 7\n",
    "n_kl = -n_kr\n",
    "r   = [-Int(N_s/4) + i for i=1:Int(N_s/2)]\n",
    "width_wp = length(r)\n",
    "xr0 = 4\n",
    "xl0 = 12\n",
    "sigma = 3/2\n",
    "\n",
    "s = siteinds(psi0)\n",
    "init_state = deepcopy(psi0)\n",
    "\n",
    "for x in 1:Int(N_s/2)\n",
    "    init_state = rz(betas_r[x], x, init_state, cutoff)\n",
    "end\n",
    "for x in 1:Int(N_s/2-1)\n",
    "    y = Int(N_s/2) - x\n",
    "    init_state = giv_op(thetas_r[x], y, y+1, init_state, cutoff)\n",
    "end\n",
    "toff = op(\"CCX\", [s[N_s+1], s[1], s[N_s+2]])\n",
    "init_state = apply(toff, init_state; cutoff)\n",
    "sm = op(\"X\", s[1]) # - 1im * op(\"Y\", s[1])\n",
    "init_state = apply(sm, init_state; cutoff)\n",
    "for x in 1:Int(N_s/2-1)\n",
    "    y = Int(N_s/2) - x\n",
    "    init_state = giv_op(-thetas_r[y], x, x+1, init_state, cutoff)\n",
    "end\n",
    "for x in 1:Int(N_s/2)\n",
    "    init_state = rz(-betas_r[x], x, init_state, cutoff)\n",
    "end\n",
    "\n",
    "\n",
    "\n",
    "for x in 1:Int(N_s/2)\n",
    "    init_state = rz(betas_l[x], x+Int(N_s/2), init_state, cutoff)\n",
    "end\n",
    "for x in 1:Int(N_s/2-1)\n",
    "    y = N_s - x\n",
    "    init_state = giv_op(thetas_l[x], y, y+1, init_state, cutoff)\n",
    "end\n",
    "for i in 1:Int(N_s/2)\n",
    "    z = op(\"Z\", s[i])\n",
    "    init_state = apply(z, init_state; cutoff)\n",
    "end\n",
    "toff = op(\"CCX\", [s[N_s+3], s[Int(N_s/2+1)], s[N_s+4]])\n",
    "init_state = apply(toff, init_state; cutoff)\n",
    "sm = op(\"X\", s[Int(N_s/2+1)]) # - 1im * op(\"Y\", s[Int(N_s/2+1)])\n",
    "init_state = apply(sm, init_state; cutoff)\n",
    "\n",
    "for x in 1:Int(N_s/2-1)\n",
    "    y = Int(N_s/2) - x\n",
    "    init_state = giv_op(-thetas_l[y], x+Int(N_s/2), x+Int(N_s/2)+1, init_state, cutoff)\n",
    "end\n",
    "for x in 1:Int(N_s/2)\n",
    "    init_state = rz(-betas_l[x], x+Int(N_s/2), init_state, cutoff)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.018618793667333045, 0.030735910125342047, 0.22555069359917934, 0.5341067323594304, 0.22555209380453395, 0.030735991444015065, 0.018619538572342942, 0.01857379057869274, 0.018620127350372995, 0.030736321460926308, 0.22555042516586815, 0.5341068624528414, 0.2255517445545751, 0.030735558086453674, 0.018618834302069787, 0.018572524223890496]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "meas_state = deepcopy(init_state)\n",
    "meas_state = apply(op(s[N_s+2], \"ProjUp\"), meas_state)\n",
    "meas_state = apply(op(s[N_s+4], \"ProjUp\"), meas_state)\n",
    "magz = expect(meas_state, \"Z\")\n",
    "occs = [(1 - magz[n])/2 for n=1:N_s]\n",
    "println(occs)\n",
    "\n",
    "sites = [n for n=1:N_s]\n",
    "plot(bar(sites, occs; label=\"TEBD\"), xlabel=\"site (s)\", ylabel=\"Occupation Number\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "96-element Vector{ITensor}:\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=793|\"S=1/2,Site,n=1\")\n",
       "Dim 2: (dim=2|id=475|\"S=1/2,Site,n=2\")\n",
       "Dim 3: (dim=2|id=793|\"S=1/2,Site,n=1\")'\n",
       "Dim 4: (dim=2|id=475|\"S=1/2,Site,n=2\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9998000066665779 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.019998666693333084im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.019998666693333084im\n",
       " 0.9998000066665779 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9998000066665778 + 0.0im\n",
       " 0.0 + 0.01999866669333308im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.01999866669333308im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9998000066665778 + 0.0im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=793|\"S=1/2,Site,n=1\")'\n",
       "Dim 2: (dim=2|id=793|\"S=1/2,Site,n=1\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9987502603949663 + 0.04997916927067833im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                     0.9987502603949663 - 0.04997916927067833im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=793|\"S=1/2,Site,n=1\")\n",
       "Dim 2: (dim=2|id=475|\"S=1/2,Site,n=2\")\n",
       "Dim 3: (dim=2|id=793|\"S=1/2,Site,n=1\")'\n",
       "Dim 4: (dim=2|id=475|\"S=1/2,Site,n=2\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999968750016276 - 0.0024999973958341475im  0.0 + 0.0im\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       " 0.9999968750016276 + 0.0024999973958341475im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im  0.9999968750016276 + 0.0024999973958341475im\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im  0.9999968750016276 - 0.0024999973958341475im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=475|\"S=1/2,Site,n=2\")\n",
       "Dim 2: (dim=2|id=580|\"S=1/2,Site,n=3\")\n",
       "Dim 3: (dim=2|id=475|\"S=1/2,Site,n=2\")'\n",
       "Dim 4: (dim=2|id=580|\"S=1/2,Site,n=3\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9998000066665779 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.019998666693333084im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.019998666693333084im\n",
       " 0.9998000066665779 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9998000066665778 + 0.0im\n",
       " 0.0 + 0.01999866669333308im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.01999866669333308im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9998000066665778 + 0.0im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=475|\"S=1/2,Site,n=2\")'\n",
       "Dim 2: (dim=2|id=475|\"S=1/2,Site,n=2\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9987502603949663 + 0.04997916927067833im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                     0.9987502603949663 - 0.04997916927067833im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=475|\"S=1/2,Site,n=2\")\n",
       "Dim 2: (dim=2|id=580|\"S=1/2,Site,n=3\")\n",
       "Dim 3: (dim=2|id=475|\"S=1/2,Site,n=2\")'\n",
       "Dim 4: (dim=2|id=580|\"S=1/2,Site,n=3\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999968750016276 - 0.0024999973958341475im  0.0 + 0.0im\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       " 0.9999968750016276 + 0.0024999973958341475im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im  0.9999968750016276 + 0.0024999973958341475im\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im  0.9999968750016276 - 0.0024999973958341475im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=580|\"S=1/2,Site,n=3\")\n",
       "Dim 2: (dim=2|id=897|\"S=1/2,Site,n=4\")\n",
       "Dim 3: (dim=2|id=580|\"S=1/2,Site,n=3\")'\n",
       "Dim 4: (dim=2|id=897|\"S=1/2,Site,n=4\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9998000066665779 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.019998666693333084im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.019998666693333084im\n",
       " 0.9998000066665779 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9998000066665778 + 0.0im\n",
       " 0.0 + 0.01999866669333308im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.01999866669333308im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9998000066665778 + 0.0im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=580|\"S=1/2,Site,n=3\")'\n",
       "Dim 2: (dim=2|id=580|\"S=1/2,Site,n=3\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9987502603949663 + 0.04997916927067833im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                     0.9987502603949663 - 0.04997916927067833im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=580|\"S=1/2,Site,n=3\")\n",
       "Dim 2: (dim=2|id=897|\"S=1/2,Site,n=4\")\n",
       "Dim 3: (dim=2|id=580|\"S=1/2,Site,n=3\")'\n",
       "Dim 4: (dim=2|id=897|\"S=1/2,Site,n=4\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999968750016276 - 0.0024999973958341475im  0.0 + 0.0im\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       " 0.9999968750016276 + 0.0024999973958341475im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im  0.9999968750016276 + 0.0024999973958341475im\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im  0.9999968750016276 - 0.0024999973958341475im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=897|\"S=1/2,Site,n=4\")\n",
       "Dim 2: (dim=2|id=202|\"S=1/2,Site,n=5\")\n",
       "Dim 3: (dim=2|id=897|\"S=1/2,Site,n=4\")'\n",
       "Dim 4: (dim=2|id=202|\"S=1/2,Site,n=5\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9998000066665779 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.019998666693333084im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.019998666693333084im\n",
       " 0.9998000066665779 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9998000066665778 + 0.0im\n",
       " 0.0 + 0.01999866669333308im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.01999866669333308im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9998000066665778 + 0.0im\n",
       " ⋮\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=580|\"S=1/2,Site,n=3\")\n",
       "Dim 2: (dim=2|id=897|\"S=1/2,Site,n=4\")\n",
       "Dim 3: (dim=2|id=580|\"S=1/2,Site,n=3\")'\n",
       "Dim 4: (dim=2|id=897|\"S=1/2,Site,n=4\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999968750016276 - 0.0024999973958341475im  0.0 + 0.0im\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       " 0.9999968750016276 + 0.0024999973958341475im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im  0.9999968750016276 + 0.0024999973958341475im\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im  0.9999968750016276 - 0.0024999973958341475im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=580|\"S=1/2,Site,n=3\")'\n",
       "Dim 2: (dim=2|id=580|\"S=1/2,Site,n=3\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9987502603949663 + 0.04997916927067833im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                     0.9987502603949663 - 0.04997916927067833im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=580|\"S=1/2,Site,n=3\")\n",
       "Dim 2: (dim=2|id=897|\"S=1/2,Site,n=4\")\n",
       "Dim 3: (dim=2|id=580|\"S=1/2,Site,n=3\")'\n",
       "Dim 4: (dim=2|id=897|\"S=1/2,Site,n=4\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9998000066665779 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.019998666693333084im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.019998666693333084im\n",
       " 0.9998000066665779 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9998000066665778 + 0.0im\n",
       " 0.0 + 0.01999866669333308im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.01999866669333308im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9998000066665778 + 0.0im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=475|\"S=1/2,Site,n=2\")\n",
       "Dim 2: (dim=2|id=580|\"S=1/2,Site,n=3\")\n",
       "Dim 3: (dim=2|id=475|\"S=1/2,Site,n=2\")'\n",
       "Dim 4: (dim=2|id=580|\"S=1/2,Site,n=3\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999968750016276 - 0.0024999973958341475im  0.0 + 0.0im\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       " 0.9999968750016276 + 0.0024999973958341475im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im  0.9999968750016276 + 0.0024999973958341475im\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im  0.9999968750016276 - 0.0024999973958341475im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=475|\"S=1/2,Site,n=2\")'\n",
       "Dim 2: (dim=2|id=475|\"S=1/2,Site,n=2\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9987502603949663 + 0.04997916927067833im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                     0.9987502603949663 - 0.04997916927067833im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=475|\"S=1/2,Site,n=2\")\n",
       "Dim 2: (dim=2|id=580|\"S=1/2,Site,n=3\")\n",
       "Dim 3: (dim=2|id=475|\"S=1/2,Site,n=2\")'\n",
       "Dim 4: (dim=2|id=580|\"S=1/2,Site,n=3\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9998000066665779 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.019998666693333084im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.019998666693333084im\n",
       " 0.9998000066665779 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9998000066665778 + 0.0im\n",
       " 0.0 + 0.01999866669333308im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.01999866669333308im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9998000066665778 + 0.0im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=793|\"S=1/2,Site,n=1\")\n",
       "Dim 2: (dim=2|id=475|\"S=1/2,Site,n=2\")\n",
       "Dim 3: (dim=2|id=793|\"S=1/2,Site,n=1\")'\n",
       "Dim 4: (dim=2|id=475|\"S=1/2,Site,n=2\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9999968750016276 - 0.0024999973958341475im  0.0 + 0.0im\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im                    0.0 + 0.0im\n",
       " 0.9999968750016276 + 0.0024999973958341475im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im  0.9999968750016276 + 0.0024999973958341475im\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.0im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im  0.9999968750016276 - 0.0024999973958341475im\n",
       " ITensor ord=2\n",
       "Dim 1: (dim=2|id=793|\"S=1/2,Site,n=1\")'\n",
       "Dim 2: (dim=2|id=793|\"S=1/2,Site,n=1\")\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2\n",
       " 0.9987502603949663 + 0.04997916927067833im  …                -0.0 + 0.0im\n",
       "               -0.0 + 0.0im                     0.9987502603949663 - 0.04997916927067833im\n",
       " ITensor ord=4\n",
       "Dim 1: (dim=2|id=793|\"S=1/2,Site,n=1\")\n",
       "Dim 2: (dim=2|id=475|\"S=1/2,Site,n=2\")\n",
       "Dim 3: (dim=2|id=793|\"S=1/2,Site,n=1\")'\n",
       "Dim 4: (dim=2|id=475|\"S=1/2,Site,n=2\")'\n",
       "NDTensors.Dense{ComplexF64, Vector{ComplexF64}}\n",
       " 2×2×2×2\n",
       "[:, :, 1, 1] =\n",
       " 0.9998000066665779 + 0.0im  0.0 + 0.0im\n",
       "                0.0 + 0.0im  0.0 + 0.019998666693333084im\n",
       "\n",
       "[:, :, 2, 1] =\n",
       "                0.0 + 0.0im  0.0 + 0.019998666693333084im\n",
       " 0.9998000066665779 + 0.0im  0.0 + 0.0im\n",
       "\n",
       "[:, :, 1, 2] =\n",
       " 0.0 + 0.0im                  0.9998000066665778 + 0.0im\n",
       " 0.0 + 0.01999866669333308im                 0.0 + 0.0im\n",
       "\n",
       "[:, :, 2, 2] =\n",
       " 0.0 + 0.01999866669333308im                 0.0 + 0.0im\n",
       " 0.0 + 0.0im                  0.9998000066665778 + 0.0im"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make Time-Evolution Circuit\n",
    "tau = 0.1\n",
    "N_t = 120\n",
    "\n",
    "gates = ITensor[]\n",
    "for j in 1:N_s\n",
    "    s1 = s[j]\n",
    "    if j == N_s\n",
    "        s2 = s[1]\n",
    "    else\n",
    "        s2 = s[j+1]\n",
    "    end\n",
    "    \n",
    "    x1 = op(\"X\", s1)\n",
    "    x2 = op(\"X\", s2)\n",
    "    hxx = - J * x1 * x2\n",
    "\n",
    "    Gj = exp(-1im * tau * hxx/2)\n",
    "\n",
    "    push!(gates, Gj)\n",
    "\n",
    "    hz = - h * op(\"Z\", s1)\n",
    "    Gj = exp(-1im * tau * hz/2)\n",
    "    push!(gates, Gj)\n",
    "\n",
    "    z1 = op(\"Z\", s1)\n",
    "    z2 = op(\"Z\", s2)\n",
    "\n",
    "    hzz = -g * z1 * z2\n",
    "\n",
    "    Gj = exp(1im * tau * hzz/2)\n",
    "    push!(gates, Gj)\n",
    "end\n",
    "\n",
    "# Include gates in reverse order too\n",
    "# (N,N-1),(N-1,N-2),...\n",
    "append!(gates, reverse(gates))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "function entropy_von_neumann(psi::MPS, b::Int)\n",
    "  s = siteinds(psi)  \n",
    "  orthogonalize!(psi, b)\n",
    "  _,S = svd(psi[b], (linkind(psi, b-1), s[b]))\n",
    "  SvN = 0.0\n",
    "  for n in 1:dim(S, 1)\n",
    "    p = S[n,n]^2\n",
    "    SvN -= p * log(p)\n",
    "  end\n",
    "  return SvN\n",
    "end\n",
    "\n",
    "# Compute and print <Sz> at each time step\n",
    "# then apply the gates to go to the next time\n",
    "# maxdim = Int(2^(N_s/2))\n",
    "maxdim = 40\n",
    "occs = []\n",
    "# EEs = []\n",
    "dims = []\n",
    "ttotal = N_t * tau\n",
    "state = init_state\n",
    "for t in 0:tau:ttotal\n",
    "    meas_state = deepcopy(state)\n",
    "    meas_state = apply(op(s[N_s+2], \"ProjUp\"), meas_state)\n",
    "    meas_state = apply(op(s[N_s+4], \"ProjUp\"), meas_state)\n",
    "    # println(\"Pass 1\")\n",
    "    Sz = expect(meas_state, \"Z\")\n",
    "    occ = [(1 - Sz[n])/2 for n=1:N_s]\n",
    "    push!(occs, occ)\n",
    "\n",
    "    # EE = []\n",
    "    # for j in 2:N_s-1\n",
    "    #   ee = ee_region(meas_state, 1:j)\n",
    "    #   push!(EE, ee)\n",
    "    # end\n",
    "    # push!(EEs, EE)\n",
    "    \n",
    "    bond_dim = maxlinkdim(meas_state)\n",
    "    push!(dims, bond_dim)\n",
    "    t ≈ ttotal && break\n",
    "\n",
    "    state = apply(gates, state; cutoff, maxdim)\n",
    "    normalize!(state)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sites = [n for n=1:N_s]\n",
    "# for p in 1:length(occs)\n",
    "#     if (p - 1) % 10 == 0\n",
    "#         plt = plot(bar(sites, occs[p]; label=\"TEBD\"); ylims= (0,0.6), xlabel=\"site\")\n",
    "#         png(plt, \"Plots/plt\" * string(p) * \".png\")\n",
    "#     end\n",
    "# end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_times = zeros((N_t+1))\n",
    "plot_occs = zeros((N_t+1, N_s))\n",
    "for i in 1:N_t+1\n",
    "    plot_times[i] = (i - 1) * tau\n",
    "    for j in 1:N_s\n",
    "        plot_occs[i,j] = occs[i][j]\n",
    "    end\n",
    "end\n",
    "\n",
    "plot_sites = zeros((N_s))\n",
    "for i in 1:N_s\n",
    "    plot_sites[i] = i\n",
    "end\n",
    "\n",
    "heatmap(plot_sites, plot_times, plot_occs, xlabel=\"site (s)\", ylabel=\"time t\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [],
   "source": [
    "title = \"Data/\"\n",
    "title *= \"ising-approxu-occs-N_s\" * string(N_s)\n",
    "title *= \"-J\" * string(J)\n",
    "title *= \"-h\" * string(h)\n",
    "title *= \"-g\" * string(g)\n",
    "title *= \"-width\" * string(sigma)\n",
    "title *= \"-dt\" * string(tau) * \".txt\"\n",
    "writedlm(title, plot_occs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"Data/ising-approxu-occs-N_s16-J0.4-h1-g0.05-width1.5-dt0.1.txt\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "title"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# EEs_mat = stack(EEs, dims=1)\n",
    "# title = \"Data/\"\n",
    "# title *= \"ising-approx-EEs-N_s\" * string(N_s)\n",
    "# title *= \"-J\" * string(J)\n",
    "# title *= \"-h\" * string(h)\n",
    "# title *= \"-g\" * string(g)\n",
    "# title *= \"-width\" * string(sigma)\n",
    "# title *= \"-dt\" * string(tau) * \".txt\"\n",
    "# writedlm(title, EEs_mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "# title"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.12.1",
   "language": "julia",
   "name": "julia-1.12"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.12.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
